相关论文: On Pivot Orbits of Boolean Functions

Given a set of endomorphisms on $\mathbb{P}^N$, we establish an upper bound on the number of points of bounded height in the associated monoid orbits. Moreover, we give a more refined estimate with an associated lower bound when the monoid…

The correlation functions for models of minimal gravity are discussed. An algorithm is proposed for calculations of invariant ratios from formulas of residues that can be compared with the coefficients of expansion of the partition function…

The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…

The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be…

Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…

In this paper we obtain several tight bounds on different types of alliance numbers of a graph: (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in the recent years. In order to translate variational models and partial differential equations to a graph,…

We generalize the notions of flippable and simultaneously flippable edges in a triangulation of a set S of points in the plane to so-called \emph{pseudo-simultaneously flippable edges}. Such edges are related to the notion of convex…

Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…

This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…

In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as…

We give an upper bound on the number of cycles in a simple graph in terms of its degree sequence, and apply this bound to resolve several conjectures of Kir\'aly and Arman and Tsaturian and to improve upper bounds on the maximum number of…

Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra. This is a development and a kind of explanation for Sklyanin's procedure of separation of…

The paper deals with planar polynomial vector fields. We aim to estimate the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for this is the second part of Hilbert's 16th problem. To…

Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the…

We prove new lower and upper bounds on the higher gonalities of finite graphs. These bounds are generalizations of known upper and lower bounds for first gonality to higher gonalities, including upper bounds on gonality involving…

We study the computation of local approximations of invariant manifolds of parabolic fixed points and parabolic periodic orbits of periodic vector fields. If the dimension of these manifolds is two or greater, in general, it is not possible…

A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the edges and a reference orientation of the graph, we…

Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…